Question: Ishaan is 3 times as old as Jessica. Four years ago, Ishaan was 5 times as old as Jessica. How old is Ishaan now?
Answer: We can use the given information to write down two equations that describe the ages of Ishaan and Jessica. Let Ishaan's current age be $i$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $i = 3j$ Four years ago, Ishaan was $i - 4$ years old, and Jessica was $j - 4$ years old. The information in the second sentence can be expressed in the following equation: $i - 4 = 5(j - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to solve our first equation for $j$ and substitute it into our second equation. Solving our first equation for $j$ , we get: $j = i / 3$ . Substituting this into our second equation, we get: $i - 4 = 5($ $(i / 3)$ $- 4)$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $i - 4 = \dfrac{5}{3} i - 20$ Solving for $i$ , we get: $\dfrac{2}{3} i = 16$ $i = \dfrac{3}{2} \cdot 16 = 24$.